A widget example of the Herfindahl-Hirschman Index

The Herfindahl-Hirschman Index, or HHI, is calculated by squaring
the market share of each company in an industry, and then adding
the squared values together. For example, assume for a minute that
the market in widgets is equally shared by 10 widget makers. Their
premerger HHI would be:

102 + 102 + 102 + 102
+ 102 + 102 + 102 + 102
+ 102 + 102 = 1,000

The highest possible HHI is 10,000 (a monopoly = 100 percent);
on the low end, an HHI can be extremely small, of course, because
the index declines with each added player and there is, conceivably,
no limit to the number that can be added.

Now suppose a merger occurred between two of them, doubling the
market share of one company, and shrinking the total market to nine
companies. In evaluating mergers, the U.S. Department of Justice
(DOJ) looks at the post-merger HHI values, which in the case of
the widget makers would be:

The DOJ also considers any increase in the HHI after the merger,
which in this case is 200. In determining whether a merger will
affect competition, the DOJ considers a HHI value under 1,000 to
be unconcentrated, and mergers within such a market are not considered
to have adverse effects on concentration.

An HHI value of 1,000 to 1,800 is considered moderately concentrated,
and increases of more than 100 points (like in the case of the widget
makers) "raise significant competitive concerns," according to DOJ
guidelines.

An HHI value of more than 1,800 is considered highly concentrated,
and a post-merger increase of more than 50 points raises red flags
with the DOJ. Using the HHI, any four-firm market share of 70 percent
would fall in the moderate to highly concentrated category, depending
on the distribution of individual market shares.